7.98/3.01	YES
8.29/3.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
8.29/3.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.29/3.02	
8.29/3.02	
8.29/3.02	Termination w.r.t. Q of the given QTRS could be proven:
8.29/3.02	
8.29/3.02	(0) QTRS
8.29/3.02	(1) QTRSToCSRProof [SOUND, 0 ms]
8.29/3.02	(2) CSR
8.29/3.02	(3) CSRRRRProof [EQUIVALENT, 99 ms]
8.29/3.02	(4) CSR
8.29/3.02	(5) CSRRRRProof [EQUIVALENT, 0 ms]
8.29/3.02	(6) CSR
8.29/3.02	(7) CSRRRRProof [EQUIVALENT, 11 ms]
8.29/3.02	(8) CSR
8.29/3.02	(9) CSRRRRProof [EQUIVALENT, 20 ms]
8.29/3.02	(10) CSR
8.29/3.02	(11) CSRRRRProof [EQUIVALENT, 11 ms]
8.29/3.02	(12) CSR
8.29/3.02	(13) CSRRRRProof [EQUIVALENT, 13 ms]
8.29/3.02	(14) CSR
8.29/3.02	(15) CSRRRRProof [EQUIVALENT, 0 ms]
8.29/3.02	(16) CSR
8.29/3.02	(17) CSRRRRProof [EQUIVALENT, 9 ms]
8.29/3.02	(18) CSR
8.29/3.02	(19) CSRRRRProof [EQUIVALENT, 0 ms]
8.29/3.02	(20) CSR
8.29/3.02	(21) CSRRRRProof [EQUIVALENT, 9 ms]
8.29/3.02	(22) CSR
8.29/3.02	(23) CSRRRRProof [EQUIVALENT, 0 ms]
8.29/3.02	(24) CSR
8.29/3.02	(25) CSRRRRProof [EQUIVALENT, 8 ms]
8.29/3.02	(26) CSR
8.29/3.02	(27) CSRRRRProof [EQUIVALENT, 0 ms]
8.29/3.02	(28) CSR
8.29/3.02	(29) CSRRRRProof [EQUIVALENT, 0 ms]
8.29/3.02	(30) CSR
8.29/3.02	(31) CSRRRRProof [EQUIVALENT, 0 ms]
8.29/3.02	(32) CSR
8.29/3.02	(33) CSRRRRProof [EQUIVALENT, 0 ms]
8.29/3.02	(34) CSR
8.29/3.02	(35) CSRRRRProof [EQUIVALENT, 0 ms]
8.29/3.02	(36) CSR
8.29/3.02	(37) CSRRRRProof [EQUIVALENT, 0 ms]
8.29/3.02	(38) CSR
8.29/3.02	(39) CSRRRRProof [EQUIVALENT, 7 ms]
8.29/3.02	(40) CSR
8.29/3.02	(41) CSRRRRProof [EQUIVALENT, 0 ms]
8.29/3.02	(42) CSR
8.29/3.02	(43) RisEmptyProof [EQUIVALENT, 0 ms]
8.29/3.02	(44) YES
8.29/3.02	
8.29/3.02	
8.29/3.02	----------------------------------------
8.29/3.02	
8.29/3.02	(0)
8.29/3.02	Obligation:
8.29/3.02	Q restricted rewrite system:
8.29/3.02	The TRS R consists of the following rules:
8.29/3.02	
8.29/3.02	   active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
8.29/3.02	   active(__(X, nil)) -> mark(X)
8.29/3.02	   active(__(nil, X)) -> mark(X)
8.29/3.02	   active(U11(tt, V)) -> mark(U12(isNeList(V)))
8.29/3.02	   active(U12(tt)) -> mark(tt)
8.29/3.02	   active(U21(tt, V1, V2)) -> mark(U22(isList(V1), V2))
8.29/3.02	   active(U22(tt, V2)) -> mark(U23(isList(V2)))
8.29/3.02	   active(U23(tt)) -> mark(tt)
8.29/3.02	   active(U31(tt, V)) -> mark(U32(isQid(V)))
8.29/3.02	   active(U32(tt)) -> mark(tt)
8.29/3.02	   active(U41(tt, V1, V2)) -> mark(U42(isList(V1), V2))
8.29/3.02	   active(U42(tt, V2)) -> mark(U43(isNeList(V2)))
8.29/3.02	   active(U43(tt)) -> mark(tt)
8.29/3.02	   active(U51(tt, V1, V2)) -> mark(U52(isNeList(V1), V2))
8.29/3.02	   active(U52(tt, V2)) -> mark(U53(isList(V2)))
8.29/3.02	   active(U53(tt)) -> mark(tt)
8.29/3.02	   active(U61(tt, V)) -> mark(U62(isQid(V)))
8.29/3.03	   active(U62(tt)) -> mark(tt)
8.29/3.03	   active(U71(tt, V)) -> mark(U72(isNePal(V)))
8.29/3.03	   active(U72(tt)) -> mark(tt)
8.29/3.03	   active(and(tt, X)) -> mark(X)
8.29/3.03	   active(isList(V)) -> mark(U11(isPalListKind(V), V))
8.29/3.03	   active(isList(nil)) -> mark(tt)
8.29/3.03	   active(isList(__(V1, V2))) -> mark(U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
8.29/3.03	   active(isNeList(V)) -> mark(U31(isPalListKind(V), V))
8.29/3.03	   active(isNeList(__(V1, V2))) -> mark(U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
8.29/3.03	   active(isNeList(__(V1, V2))) -> mark(U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
8.29/3.03	   active(isNePal(V)) -> mark(U61(isPalListKind(V), V))
8.29/3.03	   active(isNePal(__(I, __(P, I)))) -> mark(and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P))))
8.29/3.03	   active(isPal(V)) -> mark(U71(isPalListKind(V), V))
8.29/3.03	   active(isPal(nil)) -> mark(tt)
8.29/3.03	   active(isPalListKind(a)) -> mark(tt)
8.29/3.03	   active(isPalListKind(e)) -> mark(tt)
8.29/3.03	   active(isPalListKind(i)) -> mark(tt)
8.29/3.03	   active(isPalListKind(nil)) -> mark(tt)
8.29/3.03	   active(isPalListKind(o)) -> mark(tt)
8.29/3.03	   active(isPalListKind(u)) -> mark(tt)
8.29/3.03	   active(isPalListKind(__(V1, V2))) -> mark(and(isPalListKind(V1), isPalListKind(V2)))
8.29/3.03	   active(isQid(a)) -> mark(tt)
8.29/3.03	   active(isQid(e)) -> mark(tt)
8.29/3.03	   active(isQid(i)) -> mark(tt)
8.29/3.03	   active(isQid(o)) -> mark(tt)
8.29/3.03	   active(isQid(u)) -> mark(tt)
8.29/3.03	   active(__(X1, X2)) -> __(active(X1), X2)
8.29/3.03	   active(__(X1, X2)) -> __(X1, active(X2))
8.29/3.03	   active(U11(X1, X2)) -> U11(active(X1), X2)
8.29/3.03	   active(U12(X)) -> U12(active(X))
8.29/3.03	   active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3)
8.29/3.03	   active(U22(X1, X2)) -> U22(active(X1), X2)
8.29/3.03	   active(U23(X)) -> U23(active(X))
8.29/3.03	   active(U31(X1, X2)) -> U31(active(X1), X2)
8.29/3.03	   active(U32(X)) -> U32(active(X))
8.29/3.03	   active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
8.29/3.03	   active(U42(X1, X2)) -> U42(active(X1), X2)
8.29/3.03	   active(U43(X)) -> U43(active(X))
8.29/3.03	   active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3)
8.29/3.03	   active(U52(X1, X2)) -> U52(active(X1), X2)
8.29/3.03	   active(U53(X)) -> U53(active(X))
8.29/3.03	   active(U61(X1, X2)) -> U61(active(X1), X2)
8.29/3.03	   active(U62(X)) -> U62(active(X))
8.29/3.03	   active(U71(X1, X2)) -> U71(active(X1), X2)
8.29/3.03	   active(U72(X)) -> U72(active(X))
8.29/3.03	   active(and(X1, X2)) -> and(active(X1), X2)
8.29/3.03	   __(mark(X1), X2) -> mark(__(X1, X2))
8.29/3.03	   __(X1, mark(X2)) -> mark(__(X1, X2))
8.29/3.03	   U11(mark(X1), X2) -> mark(U11(X1, X2))
8.29/3.03	   U12(mark(X)) -> mark(U12(X))
8.29/3.03	   U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3))
8.29/3.03	   U22(mark(X1), X2) -> mark(U22(X1, X2))
8.29/3.03	   U23(mark(X)) -> mark(U23(X))
8.29/3.03	   U31(mark(X1), X2) -> mark(U31(X1, X2))
8.29/3.03	   U32(mark(X)) -> mark(U32(X))
8.29/3.03	   U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
8.29/3.03	   U42(mark(X1), X2) -> mark(U42(X1, X2))
8.29/3.03	   U43(mark(X)) -> mark(U43(X))
8.29/3.03	   U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3))
8.29/3.03	   U52(mark(X1), X2) -> mark(U52(X1, X2))
8.29/3.03	   U53(mark(X)) -> mark(U53(X))
8.29/3.03	   U61(mark(X1), X2) -> mark(U61(X1, X2))
8.29/3.03	   U62(mark(X)) -> mark(U62(X))
8.29/3.03	   U71(mark(X1), X2) -> mark(U71(X1, X2))
8.29/3.03	   U72(mark(X)) -> mark(U72(X))
8.29/3.03	   and(mark(X1), X2) -> mark(and(X1, X2))
8.29/3.03	   proper(__(X1, X2)) -> __(proper(X1), proper(X2))
8.29/3.03	   proper(nil) -> ok(nil)
8.29/3.03	   proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
8.29/3.03	   proper(tt) -> ok(tt)
8.29/3.03	   proper(U12(X)) -> U12(proper(X))
8.29/3.03	   proper(isNeList(X)) -> isNeList(proper(X))
8.29/3.03	   proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3))
8.29/3.03	   proper(U22(X1, X2)) -> U22(proper(X1), proper(X2))
8.29/3.03	   proper(isList(X)) -> isList(proper(X))
8.29/3.03	   proper(U23(X)) -> U23(proper(X))
8.29/3.03	   proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
8.29/3.03	   proper(U32(X)) -> U32(proper(X))
8.29/3.03	   proper(isQid(X)) -> isQid(proper(X))
8.29/3.03	   proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3))
8.29/3.03	   proper(U42(X1, X2)) -> U42(proper(X1), proper(X2))
8.29/3.03	   proper(U43(X)) -> U43(proper(X))
8.29/3.03	   proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3))
8.29/3.03	   proper(U52(X1, X2)) -> U52(proper(X1), proper(X2))
8.29/3.03	   proper(U53(X)) -> U53(proper(X))
8.29/3.03	   proper(U61(X1, X2)) -> U61(proper(X1), proper(X2))
8.29/3.03	   proper(U62(X)) -> U62(proper(X))
8.29/3.03	   proper(U71(X1, X2)) -> U71(proper(X1), proper(X2))
8.29/3.03	   proper(U72(X)) -> U72(proper(X))
8.29/3.03	   proper(isNePal(X)) -> isNePal(proper(X))
8.29/3.03	   proper(and(X1, X2)) -> and(proper(X1), proper(X2))
8.29/3.03	   proper(isPalListKind(X)) -> isPalListKind(proper(X))
8.29/3.03	   proper(isPal(X)) -> isPal(proper(X))
8.29/3.03	   proper(a) -> ok(a)
8.29/3.03	   proper(e) -> ok(e)
8.29/3.03	   proper(i) -> ok(i)
8.29/3.03	   proper(o) -> ok(o)
8.29/3.03	   proper(u) -> ok(u)
8.29/3.03	   __(ok(X1), ok(X2)) -> ok(__(X1, X2))
8.29/3.03	   U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
8.29/3.03	   U12(ok(X)) -> ok(U12(X))
8.29/3.03	   isNeList(ok(X)) -> ok(isNeList(X))
8.29/3.03	   U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3))
8.29/3.03	   U22(ok(X1), ok(X2)) -> ok(U22(X1, X2))
8.29/3.03	   isList(ok(X)) -> ok(isList(X))
8.29/3.03	   U23(ok(X)) -> ok(U23(X))
8.29/3.03	   U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
8.29/3.03	   U32(ok(X)) -> ok(U32(X))
8.29/3.03	   isQid(ok(X)) -> ok(isQid(X))
8.29/3.03	   U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
8.29/3.03	   U42(ok(X1), ok(X2)) -> ok(U42(X1, X2))
8.29/3.03	   U43(ok(X)) -> ok(U43(X))
8.29/3.03	   U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3))
8.29/3.03	   U52(ok(X1), ok(X2)) -> ok(U52(X1, X2))
8.29/3.03	   U53(ok(X)) -> ok(U53(X))
8.29/3.03	   U61(ok(X1), ok(X2)) -> ok(U61(X1, X2))
8.29/3.03	   U62(ok(X)) -> ok(U62(X))
8.29/3.03	   U71(ok(X1), ok(X2)) -> ok(U71(X1, X2))
8.29/3.03	   U72(ok(X)) -> ok(U72(X))
8.29/3.03	   isNePal(ok(X)) -> ok(isNePal(X))
8.29/3.03	   and(ok(X1), ok(X2)) -> ok(and(X1, X2))
8.29/3.03	   isPalListKind(ok(X)) -> ok(isPalListKind(X))
8.29/3.03	   isPal(ok(X)) -> ok(isPal(X))
8.29/3.03	   top(mark(X)) -> top(proper(X))
8.29/3.03	   top(ok(X)) -> top(active(X))
8.29/3.03	
8.29/3.03	The set Q consists of the following terms:
8.29/3.03	
8.29/3.03	   active(isList(x0))
8.29/3.03	   active(isNeList(x0))
8.29/3.03	   active(isNePal(x0))
8.29/3.03	   active(isPal(x0))
8.29/3.03	   active(isPalListKind(a))
8.29/3.03	   active(isPalListKind(e))
8.29/3.03	   active(isPalListKind(i))
8.29/3.03	   active(isPalListKind(nil))
8.29/3.03	   active(isPalListKind(o))
8.29/3.03	   active(isPalListKind(u))
8.29/3.03	   active(isPalListKind(__(x0, x1)))
8.29/3.03	   active(isQid(a))
8.29/3.03	   active(isQid(e))
8.29/3.03	   active(isQid(i))
8.29/3.03	   active(isQid(o))
8.29/3.03	   active(isQid(u))
8.29/3.03	   active(__(x0, x1))
8.29/3.03	   active(U11(x0, x1))
8.29/3.03	   active(U12(x0))
8.29/3.03	   active(U21(x0, x1, x2))
8.29/3.03	   active(U22(x0, x1))
8.29/3.03	   active(U23(x0))
8.29/3.03	   active(U31(x0, x1))
8.29/3.03	   active(U32(x0))
8.29/3.03	   active(U41(x0, x1, x2))
8.29/3.03	   active(U42(x0, x1))
8.29/3.03	   active(U43(x0))
8.29/3.03	   active(U51(x0, x1, x2))
8.29/3.03	   active(U52(x0, x1))
8.29/3.03	   active(U53(x0))
8.29/3.03	   active(U61(x0, x1))
8.29/3.03	   active(U62(x0))
8.29/3.03	   active(U71(x0, x1))
8.29/3.03	   active(U72(x0))
8.29/3.03	   active(and(x0, x1))
8.29/3.03	   __(mark(x0), x1)
8.29/3.03	   __(x0, mark(x1))
8.29/3.03	   U11(mark(x0), x1)
8.29/3.03	   U12(mark(x0))
8.29/3.03	   U21(mark(x0), x1, x2)
8.29/3.03	   U22(mark(x0), x1)
8.29/3.03	   U23(mark(x0))
8.29/3.03	   U31(mark(x0), x1)
8.29/3.03	   U32(mark(x0))
8.29/3.03	   U41(mark(x0), x1, x2)
8.29/3.03	   U42(mark(x0), x1)
8.29/3.03	   U43(mark(x0))
8.29/3.03	   U51(mark(x0), x1, x2)
8.29/3.03	   U52(mark(x0), x1)
8.29/3.03	   U53(mark(x0))
8.29/3.03	   U61(mark(x0), x1)
8.29/3.03	   U62(mark(x0))
8.29/3.03	   U71(mark(x0), x1)
8.29/3.03	   U72(mark(x0))
8.29/3.03	   and(mark(x0), x1)
8.29/3.03	   proper(__(x0, x1))
8.29/3.03	   proper(nil)
8.29/3.03	   proper(U11(x0, x1))
8.29/3.03	   proper(tt)
8.29/3.03	   proper(U12(x0))
8.29/3.03	   proper(isNeList(x0))
8.29/3.03	   proper(U21(x0, x1, x2))
8.29/3.03	   proper(U22(x0, x1))
8.29/3.03	   proper(isList(x0))
8.29/3.03	   proper(U23(x0))
8.29/3.03	   proper(U31(x0, x1))
8.29/3.03	   proper(U32(x0))
8.29/3.03	   proper(isQid(x0))
8.29/3.03	   proper(U41(x0, x1, x2))
8.29/3.03	   proper(U42(x0, x1))
8.29/3.03	   proper(U43(x0))
8.29/3.03	   proper(U51(x0, x1, x2))
8.29/3.03	   proper(U52(x0, x1))
8.29/3.03	   proper(U53(x0))
8.29/3.03	   proper(U61(x0, x1))
8.29/3.03	   proper(U62(x0))
8.29/3.03	   proper(U71(x0, x1))
8.29/3.03	   proper(U72(x0))
8.29/3.03	   proper(isNePal(x0))
8.29/3.03	   proper(and(x0, x1))
8.29/3.03	   proper(isPalListKind(x0))
8.29/3.03	   proper(isPal(x0))
8.29/3.03	   proper(a)
8.29/3.03	   proper(e)
8.29/3.03	   proper(i)
8.29/3.03	   proper(o)
8.29/3.03	   proper(u)
8.29/3.03	   __(ok(x0), ok(x1))
8.29/3.03	   U11(ok(x0), ok(x1))
8.29/3.03	   U12(ok(x0))
8.29/3.03	   isNeList(ok(x0))
8.29/3.03	   U21(ok(x0), ok(x1), ok(x2))
8.29/3.03	   U22(ok(x0), ok(x1))
8.29/3.03	   isList(ok(x0))
8.29/3.03	   U23(ok(x0))
8.29/3.03	   U31(ok(x0), ok(x1))
8.29/3.03	   U32(ok(x0))
8.29/3.03	   isQid(ok(x0))
8.29/3.03	   U41(ok(x0), ok(x1), ok(x2))
8.29/3.03	   U42(ok(x0), ok(x1))
8.29/3.03	   U43(ok(x0))
8.29/3.03	   U51(ok(x0), ok(x1), ok(x2))
8.29/3.03	   U52(ok(x0), ok(x1))
8.29/3.03	   U53(ok(x0))
8.29/3.03	   U61(ok(x0), ok(x1))
8.29/3.03	   U62(ok(x0))
8.29/3.03	   U71(ok(x0), ok(x1))
8.29/3.03	   U72(ok(x0))
8.29/3.03	   isNePal(ok(x0))
8.29/3.03	   and(ok(x0), ok(x1))
8.29/3.03	   isPalListKind(ok(x0))
8.29/3.03	   isPal(ok(x0))
8.29/3.03	   top(mark(x0))
8.29/3.03	   top(ok(x0))
8.29/3.03	
8.29/3.03	
8.29/3.03	----------------------------------------
8.29/3.03	
8.29/3.03	(1) QTRSToCSRProof (SOUND)
8.29/3.03	The following Q TRS is given: Q restricted rewrite system:
8.29/3.03	The TRS R consists of the following rules:
8.29/3.03	
8.29/3.03	   active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z)))
8.29/3.03	   active(__(X, nil)) -> mark(X)
8.29/3.03	   active(__(nil, X)) -> mark(X)
8.29/3.03	   active(U11(tt, V)) -> mark(U12(isNeList(V)))
8.29/3.03	   active(U12(tt)) -> mark(tt)
8.29/3.03	   active(U21(tt, V1, V2)) -> mark(U22(isList(V1), V2))
8.29/3.03	   active(U22(tt, V2)) -> mark(U23(isList(V2)))
8.29/3.03	   active(U23(tt)) -> mark(tt)
8.29/3.03	   active(U31(tt, V)) -> mark(U32(isQid(V)))
8.29/3.03	   active(U32(tt)) -> mark(tt)
8.29/3.03	   active(U41(tt, V1, V2)) -> mark(U42(isList(V1), V2))
8.29/3.03	   active(U42(tt, V2)) -> mark(U43(isNeList(V2)))
8.29/3.03	   active(U43(tt)) -> mark(tt)
8.29/3.03	   active(U51(tt, V1, V2)) -> mark(U52(isNeList(V1), V2))
8.29/3.03	   active(U52(tt, V2)) -> mark(U53(isList(V2)))
8.29/3.03	   active(U53(tt)) -> mark(tt)
8.29/3.03	   active(U61(tt, V)) -> mark(U62(isQid(V)))
8.29/3.03	   active(U62(tt)) -> mark(tt)
8.29/3.03	   active(U71(tt, V)) -> mark(U72(isNePal(V)))
8.29/3.03	   active(U72(tt)) -> mark(tt)
8.29/3.03	   active(and(tt, X)) -> mark(X)
8.29/3.03	   active(isList(V)) -> mark(U11(isPalListKind(V), V))
8.29/3.03	   active(isList(nil)) -> mark(tt)
8.29/3.03	   active(isList(__(V1, V2))) -> mark(U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
8.29/3.03	   active(isNeList(V)) -> mark(U31(isPalListKind(V), V))
8.29/3.03	   active(isNeList(__(V1, V2))) -> mark(U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
8.29/3.03	   active(isNeList(__(V1, V2))) -> mark(U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2))
8.29/3.03	   active(isNePal(V)) -> mark(U61(isPalListKind(V), V))
8.29/3.03	   active(isNePal(__(I, __(P, I)))) -> mark(and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P))))
8.29/3.03	   active(isPal(V)) -> mark(U71(isPalListKind(V), V))
8.29/3.03	   active(isPal(nil)) -> mark(tt)
8.29/3.03	   active(isPalListKind(a)) -> mark(tt)
8.29/3.03	   active(isPalListKind(e)) -> mark(tt)
8.29/3.03	   active(isPalListKind(i)) -> mark(tt)
8.29/3.03	   active(isPalListKind(nil)) -> mark(tt)
8.29/3.03	   active(isPalListKind(o)) -> mark(tt)
8.29/3.03	   active(isPalListKind(u)) -> mark(tt)
8.29/3.03	   active(isPalListKind(__(V1, V2))) -> mark(and(isPalListKind(V1), isPalListKind(V2)))
8.29/3.03	   active(isQid(a)) -> mark(tt)
8.29/3.03	   active(isQid(e)) -> mark(tt)
8.29/3.03	   active(isQid(i)) -> mark(tt)
8.29/3.03	   active(isQid(o)) -> mark(tt)
8.29/3.03	   active(isQid(u)) -> mark(tt)
8.29/3.03	   active(__(X1, X2)) -> __(active(X1), X2)
8.29/3.03	   active(__(X1, X2)) -> __(X1, active(X2))
8.29/3.03	   active(U11(X1, X2)) -> U11(active(X1), X2)
8.29/3.03	   active(U12(X)) -> U12(active(X))
8.29/3.03	   active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3)
8.29/3.03	   active(U22(X1, X2)) -> U22(active(X1), X2)
8.29/3.03	   active(U23(X)) -> U23(active(X))
8.29/3.03	   active(U31(X1, X2)) -> U31(active(X1), X2)
8.29/3.03	   active(U32(X)) -> U32(active(X))
8.29/3.03	   active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
8.29/3.03	   active(U42(X1, X2)) -> U42(active(X1), X2)
8.29/3.03	   active(U43(X)) -> U43(active(X))
8.29/3.03	   active(U51(X1, X2, X3)) -> U51(active(X1), X2, X3)
8.29/3.03	   active(U52(X1, X2)) -> U52(active(X1), X2)
8.29/3.03	   active(U53(X)) -> U53(active(X))
8.29/3.03	   active(U61(X1, X2)) -> U61(active(X1), X2)
8.29/3.03	   active(U62(X)) -> U62(active(X))
8.29/3.03	   active(U71(X1, X2)) -> U71(active(X1), X2)
8.29/3.03	   active(U72(X)) -> U72(active(X))
8.29/3.03	   active(and(X1, X2)) -> and(active(X1), X2)
8.29/3.03	   __(mark(X1), X2) -> mark(__(X1, X2))
8.29/3.03	   __(X1, mark(X2)) -> mark(__(X1, X2))
8.29/3.03	   U11(mark(X1), X2) -> mark(U11(X1, X2))
8.29/3.03	   U12(mark(X)) -> mark(U12(X))
8.29/3.03	   U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3))
8.29/3.03	   U22(mark(X1), X2) -> mark(U22(X1, X2))
8.29/3.03	   U23(mark(X)) -> mark(U23(X))
8.29/3.03	   U31(mark(X1), X2) -> mark(U31(X1, X2))
8.29/3.03	   U32(mark(X)) -> mark(U32(X))
8.29/3.03	   U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
8.29/3.03	   U42(mark(X1), X2) -> mark(U42(X1, X2))
8.29/3.03	   U43(mark(X)) -> mark(U43(X))
8.29/3.03	   U51(mark(X1), X2, X3) -> mark(U51(X1, X2, X3))
8.29/3.03	   U52(mark(X1), X2) -> mark(U52(X1, X2))
8.29/3.03	   U53(mark(X)) -> mark(U53(X))
8.29/3.03	   U61(mark(X1), X2) -> mark(U61(X1, X2))
8.29/3.03	   U62(mark(X)) -> mark(U62(X))
8.29/3.03	   U71(mark(X1), X2) -> mark(U71(X1, X2))
8.29/3.03	   U72(mark(X)) -> mark(U72(X))
8.29/3.03	   and(mark(X1), X2) -> mark(and(X1, X2))
8.29/3.03	   proper(__(X1, X2)) -> __(proper(X1), proper(X2))
8.29/3.03	   proper(nil) -> ok(nil)
8.29/3.03	   proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
8.29/3.03	   proper(tt) -> ok(tt)
8.29/3.03	   proper(U12(X)) -> U12(proper(X))
8.29/3.03	   proper(isNeList(X)) -> isNeList(proper(X))
8.29/3.03	   proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3))
8.29/3.03	   proper(U22(X1, X2)) -> U22(proper(X1), proper(X2))
8.29/3.03	   proper(isList(X)) -> isList(proper(X))
8.29/3.03	   proper(U23(X)) -> U23(proper(X))
8.29/3.03	   proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
8.29/3.03	   proper(U32(X)) -> U32(proper(X))
8.29/3.03	   proper(isQid(X)) -> isQid(proper(X))
8.29/3.03	   proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3))
8.29/3.03	   proper(U42(X1, X2)) -> U42(proper(X1), proper(X2))
8.29/3.03	   proper(U43(X)) -> U43(proper(X))
8.29/3.03	   proper(U51(X1, X2, X3)) -> U51(proper(X1), proper(X2), proper(X3))
8.29/3.03	   proper(U52(X1, X2)) -> U52(proper(X1), proper(X2))
8.29/3.03	   proper(U53(X)) -> U53(proper(X))
8.29/3.03	   proper(U61(X1, X2)) -> U61(proper(X1), proper(X2))
8.29/3.03	   proper(U62(X)) -> U62(proper(X))
8.29/3.03	   proper(U71(X1, X2)) -> U71(proper(X1), proper(X2))
8.29/3.03	   proper(U72(X)) -> U72(proper(X))
8.29/3.03	   proper(isNePal(X)) -> isNePal(proper(X))
8.29/3.03	   proper(and(X1, X2)) -> and(proper(X1), proper(X2))
8.29/3.03	   proper(isPalListKind(X)) -> isPalListKind(proper(X))
8.29/3.03	   proper(isPal(X)) -> isPal(proper(X))
8.29/3.03	   proper(a) -> ok(a)
8.29/3.03	   proper(e) -> ok(e)
8.29/3.03	   proper(i) -> ok(i)
8.29/3.03	   proper(o) -> ok(o)
8.29/3.03	   proper(u) -> ok(u)
8.29/3.03	   __(ok(X1), ok(X2)) -> ok(__(X1, X2))
8.29/3.03	   U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
8.29/3.03	   U12(ok(X)) -> ok(U12(X))
8.29/3.03	   isNeList(ok(X)) -> ok(isNeList(X))
8.29/3.03	   U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3))
8.29/3.03	   U22(ok(X1), ok(X2)) -> ok(U22(X1, X2))
8.29/3.03	   isList(ok(X)) -> ok(isList(X))
8.29/3.03	   U23(ok(X)) -> ok(U23(X))
8.29/3.03	   U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
8.29/3.03	   U32(ok(X)) -> ok(U32(X))
8.29/3.03	   isQid(ok(X)) -> ok(isQid(X))
8.29/3.03	   U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
8.29/3.03	   U42(ok(X1), ok(X2)) -> ok(U42(X1, X2))
8.29/3.03	   U43(ok(X)) -> ok(U43(X))
8.29/3.03	   U51(ok(X1), ok(X2), ok(X3)) -> ok(U51(X1, X2, X3))
8.29/3.03	   U52(ok(X1), ok(X2)) -> ok(U52(X1, X2))
8.29/3.03	   U53(ok(X)) -> ok(U53(X))
8.29/3.03	   U61(ok(X1), ok(X2)) -> ok(U61(X1, X2))
8.29/3.03	   U62(ok(X)) -> ok(U62(X))
8.29/3.03	   U71(ok(X1), ok(X2)) -> ok(U71(X1, X2))
8.29/3.03	   U72(ok(X)) -> ok(U72(X))
8.29/3.03	   isNePal(ok(X)) -> ok(isNePal(X))
8.29/3.03	   and(ok(X1), ok(X2)) -> ok(and(X1, X2))
8.29/3.03	   isPalListKind(ok(X)) -> ok(isPalListKind(X))
8.29/3.03	   isPal(ok(X)) -> ok(isPal(X))
8.29/3.03	   top(mark(X)) -> top(proper(X))
8.29/3.03	   top(ok(X)) -> top(active(X))
8.29/3.03	
8.29/3.03	The set Q consists of the following terms:
8.29/3.03	
8.29/3.03	   active(isList(x0))
8.29/3.03	   active(isNeList(x0))
8.29/3.03	   active(isNePal(x0))
8.29/3.03	   active(isPal(x0))
8.29/3.03	   active(isPalListKind(a))
8.29/3.03	   active(isPalListKind(e))
8.29/3.03	   active(isPalListKind(i))
8.29/3.03	   active(isPalListKind(nil))
8.29/3.03	   active(isPalListKind(o))
8.29/3.03	   active(isPalListKind(u))
8.29/3.03	   active(isPalListKind(__(x0, x1)))
8.29/3.03	   active(isQid(a))
8.29/3.03	   active(isQid(e))
8.29/3.03	   active(isQid(i))
8.29/3.03	   active(isQid(o))
8.29/3.03	   active(isQid(u))
8.29/3.03	   active(__(x0, x1))
8.29/3.03	   active(U11(x0, x1))
8.29/3.03	   active(U12(x0))
8.29/3.03	   active(U21(x0, x1, x2))
8.29/3.03	   active(U22(x0, x1))
8.29/3.03	   active(U23(x0))
8.29/3.03	   active(U31(x0, x1))
8.29/3.03	   active(U32(x0))
8.29/3.03	   active(U41(x0, x1, x2))
8.29/3.03	   active(U42(x0, x1))
8.29/3.03	   active(U43(x0))
8.29/3.03	   active(U51(x0, x1, x2))
8.29/3.03	   active(U52(x0, x1))
8.29/3.03	   active(U53(x0))
8.29/3.03	   active(U61(x0, x1))
8.29/3.03	   active(U62(x0))
8.29/3.03	   active(U71(x0, x1))
8.29/3.03	   active(U72(x0))
8.29/3.03	   active(and(x0, x1))
8.29/3.03	   __(mark(x0), x1)
8.29/3.03	   __(x0, mark(x1))
8.29/3.03	   U11(mark(x0), x1)
8.29/3.03	   U12(mark(x0))
8.29/3.03	   U21(mark(x0), x1, x2)
8.29/3.03	   U22(mark(x0), x1)
8.29/3.03	   U23(mark(x0))
8.29/3.03	   U31(mark(x0), x1)
8.29/3.03	   U32(mark(x0))
8.29/3.03	   U41(mark(x0), x1, x2)
8.29/3.03	   U42(mark(x0), x1)
8.29/3.03	   U43(mark(x0))
8.29/3.03	   U51(mark(x0), x1, x2)
8.29/3.03	   U52(mark(x0), x1)
8.29/3.03	   U53(mark(x0))
8.29/3.03	   U61(mark(x0), x1)
8.29/3.03	   U62(mark(x0))
8.29/3.03	   U71(mark(x0), x1)
8.29/3.03	   U72(mark(x0))
8.29/3.03	   and(mark(x0), x1)
8.29/3.03	   proper(__(x0, x1))
8.29/3.03	   proper(nil)
8.29/3.03	   proper(U11(x0, x1))
8.29/3.03	   proper(tt)
8.29/3.03	   proper(U12(x0))
8.29/3.03	   proper(isNeList(x0))
8.29/3.03	   proper(U21(x0, x1, x2))
8.29/3.03	   proper(U22(x0, x1))
8.29/3.03	   proper(isList(x0))
8.29/3.03	   proper(U23(x0))
8.29/3.03	   proper(U31(x0, x1))
8.29/3.03	   proper(U32(x0))
8.29/3.03	   proper(isQid(x0))
8.29/3.03	   proper(U41(x0, x1, x2))
8.29/3.03	   proper(U42(x0, x1))
8.29/3.03	   proper(U43(x0))
8.29/3.03	   proper(U51(x0, x1, x2))
8.29/3.03	   proper(U52(x0, x1))
8.29/3.03	   proper(U53(x0))
8.29/3.03	   proper(U61(x0, x1))
8.29/3.03	   proper(U62(x0))
8.29/3.03	   proper(U71(x0, x1))
8.29/3.03	   proper(U72(x0))
8.29/3.03	   proper(isNePal(x0))
8.29/3.03	   proper(and(x0, x1))
8.29/3.03	   proper(isPalListKind(x0))
8.29/3.03	   proper(isPal(x0))
8.29/3.03	   proper(a)
8.29/3.03	   proper(e)
8.29/3.03	   proper(i)
8.29/3.03	   proper(o)
8.29/3.03	   proper(u)
8.29/3.03	   __(ok(x0), ok(x1))
8.29/3.03	   U11(ok(x0), ok(x1))
8.29/3.03	   U12(ok(x0))
8.29/3.03	   isNeList(ok(x0))
8.29/3.03	   U21(ok(x0), ok(x1), ok(x2))
8.29/3.03	   U22(ok(x0), ok(x1))
8.29/3.03	   isList(ok(x0))
8.29/3.03	   U23(ok(x0))
8.29/3.03	   U31(ok(x0), ok(x1))
8.29/3.03	   U32(ok(x0))
8.29/3.03	   isQid(ok(x0))
8.29/3.03	   U41(ok(x0), ok(x1), ok(x2))
8.29/3.03	   U42(ok(x0), ok(x1))
8.29/3.03	   U43(ok(x0))
8.29/3.03	   U51(ok(x0), ok(x1), ok(x2))
8.29/3.03	   U52(ok(x0), ok(x1))
8.29/3.03	   U53(ok(x0))
8.29/3.03	   U61(ok(x0), ok(x1))
8.29/3.03	   U62(ok(x0))
8.29/3.03	   U71(ok(x0), ok(x1))
8.29/3.03	   U72(ok(x0))
8.29/3.03	   isNePal(ok(x0))
8.29/3.03	   and(ok(x0), ok(x1))
8.29/3.03	   isPalListKind(ok(x0))
8.29/3.03	   isPal(ok(x0))
8.29/3.03	   top(mark(x0))
8.29/3.03	   top(ok(x0))
8.29/3.03	
8.29/3.03	Special symbols used for the transformation (see [GM04]):
8.29/3.03	top: top_1, active: active_1, mark: mark_1, ok: ok_1, proper: proper_1
8.29/3.03	The replacement map contains the following entries:
8.29/3.03	
8.29/3.03	__: {1, 2}
8.29/3.03	nil: empty set
8.29/3.03	U11: {1}
8.29/3.03	tt: empty set
8.29/3.03	U12: {1}
8.29/3.03	isNeList: empty set
8.29/3.03	U21: {1}
8.29/3.03	U22: {1}
8.29/3.03	isList: empty set
8.29/3.03	U23: {1}
8.29/3.03	U31: {1}
8.29/3.03	U32: {1}
8.29/3.03	isQid: empty set
8.29/3.03	U41: {1}
8.29/3.03	U42: {1}
8.29/3.03	U43: {1}
8.29/3.03	U51: {1}
8.29/3.03	U52: {1}
8.29/3.03	U53: {1}
8.29/3.03	U61: {1}
8.29/3.03	U62: {1}
8.29/3.03	U71: {1}
8.29/3.03	U72: {1}
8.29/3.03	isNePal: empty set
8.29/3.03	and: {1}
8.29/3.03	isPalListKind: empty set
8.29/3.03	isPal: empty set
8.29/3.03	a: empty set
8.29/3.03	e: empty set
8.29/3.03	i: empty set
8.29/3.03	o: empty set
8.29/3.03	u: empty set
8.29/3.03	The QTRS contained just a subset of rules created by the complete Giesl-Middeldorp transformation. Therefore, the inverse transformation is sound, but not necessarily complete.
8.29/3.03	----------------------------------------
8.29/3.03	
8.29/3.03	(2)
8.29/3.03	Obligation:
8.29/3.03	Context-sensitive rewrite system:
8.29/3.03	The TRS R consists of the following rules:
8.29/3.03	
8.29/3.03	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.03	   __(X, nil) -> X
8.29/3.03	   __(nil, X) -> X
8.29/3.03	   U11(tt, V) -> U12(isNeList(V))
8.29/3.03	   U12(tt) -> tt
8.29/3.03	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.03	   U22(tt, V2) -> U23(isList(V2))
8.29/3.03	   U23(tt) -> tt
8.29/3.03	   U31(tt, V) -> U32(isQid(V))
8.29/3.03	   U32(tt) -> tt
8.29/3.03	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.03	   U42(tt, V2) -> U43(isNeList(V2))
8.29/3.03	   U43(tt) -> tt
8.29/3.03	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.03	   U52(tt, V2) -> U53(isList(V2))
8.29/3.03	   U53(tt) -> tt
8.29/3.03	   U61(tt, V) -> U62(isQid(V))
8.29/3.03	   U62(tt) -> tt
8.29/3.03	   U71(tt, V) -> U72(isNePal(V))
8.29/3.03	   U72(tt) -> tt
8.29/3.03	   and(tt, X) -> X
8.29/3.03	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.03	   isList(nil) -> tt
8.29/3.03	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.03	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.03	   isNePal(__(I, __(P, I))) -> and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))
8.29/3.03	   isPal(V) -> U71(isPalListKind(V), V)
8.29/3.03	   isPal(nil) -> tt
8.29/3.03	   isPalListKind(a) -> tt
8.29/3.03	   isPalListKind(e) -> tt
8.29/3.03	   isPalListKind(i) -> tt
8.29/3.03	   isPalListKind(nil) -> tt
8.29/3.03	   isPalListKind(o) -> tt
8.29/3.03	   isPalListKind(u) -> tt
8.29/3.03	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.03	   isQid(a) -> tt
8.29/3.03	   isQid(e) -> tt
8.29/3.03	   isQid(i) -> tt
8.29/3.03	   isQid(o) -> tt
8.29/3.03	   isQid(u) -> tt
8.29/3.03	
8.29/3.03	The replacement map contains the following entries:
8.29/3.03	
8.29/3.03	__: {1, 2}
8.29/3.03	nil: empty set
8.29/3.03	U11: {1}
8.29/3.03	tt: empty set
8.29/3.03	U12: {1}
8.29/3.03	isNeList: empty set
8.29/3.03	U21: {1}
8.29/3.03	U22: {1}
8.29/3.03	isList: empty set
8.29/3.03	U23: {1}
8.29/3.03	U31: {1}
8.29/3.03	U32: {1}
8.29/3.03	isQid: empty set
8.29/3.03	U41: {1}
8.29/3.03	U42: {1}
8.29/3.03	U43: {1}
8.29/3.03	U51: {1}
8.29/3.03	U52: {1}
8.29/3.03	U53: {1}
8.29/3.03	U61: {1}
8.29/3.03	U62: {1}
8.29/3.03	U71: {1}
8.29/3.03	U72: {1}
8.29/3.03	isNePal: empty set
8.29/3.03	and: {1}
8.29/3.03	isPalListKind: empty set
8.29/3.03	isPal: empty set
8.29/3.03	a: empty set
8.29/3.03	e: empty set
8.29/3.03	i: empty set
8.29/3.03	o: empty set
8.29/3.03	u: empty set
8.29/3.03	
8.29/3.03	----------------------------------------
8.29/3.03	
8.29/3.03	(3) CSRRRRProof (EQUIVALENT)
8.29/3.03	The following CSR is given: Context-sensitive rewrite system:
8.29/3.03	The TRS R consists of the following rules:
8.29/3.03	
8.29/3.03	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.03	   __(X, nil) -> X
8.29/3.03	   __(nil, X) -> X
8.29/3.03	   U11(tt, V) -> U12(isNeList(V))
8.29/3.03	   U12(tt) -> tt
8.29/3.03	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.03	   U22(tt, V2) -> U23(isList(V2))
8.29/3.03	   U23(tt) -> tt
8.29/3.03	   U31(tt, V) -> U32(isQid(V))
8.29/3.03	   U32(tt) -> tt
8.29/3.03	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.03	   U42(tt, V2) -> U43(isNeList(V2))
8.29/3.03	   U43(tt) -> tt
8.29/3.03	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.03	   U52(tt, V2) -> U53(isList(V2))
8.29/3.03	   U53(tt) -> tt
8.29/3.03	   U61(tt, V) -> U62(isQid(V))
8.29/3.03	   U62(tt) -> tt
8.29/3.03	   U71(tt, V) -> U72(isNePal(V))
8.29/3.03	   U72(tt) -> tt
8.29/3.03	   and(tt, X) -> X
8.29/3.03	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.03	   isList(nil) -> tt
8.29/3.03	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.03	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.03	   isNePal(__(I, __(P, I))) -> and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))
8.29/3.03	   isPal(V) -> U71(isPalListKind(V), V)
8.29/3.03	   isPal(nil) -> tt
8.29/3.03	   isPalListKind(a) -> tt
8.29/3.03	   isPalListKind(e) -> tt
8.29/3.03	   isPalListKind(i) -> tt
8.29/3.03	   isPalListKind(nil) -> tt
8.29/3.03	   isPalListKind(o) -> tt
8.29/3.03	   isPalListKind(u) -> tt
8.29/3.03	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.03	   isQid(a) -> tt
8.29/3.03	   isQid(e) -> tt
8.29/3.03	   isQid(i) -> tt
8.29/3.03	   isQid(o) -> tt
8.29/3.03	   isQid(u) -> tt
8.29/3.03	
8.29/3.03	The replacement map contains the following entries:
8.29/3.03	
8.29/3.03	__: {1, 2}
8.29/3.03	nil: empty set
8.29/3.03	U11: {1}
8.29/3.03	tt: empty set
8.29/3.03	U12: {1}
8.29/3.03	isNeList: empty set
8.29/3.03	U21: {1}
8.29/3.03	U22: {1}
8.29/3.03	isList: empty set
8.29/3.03	U23: {1}
8.29/3.03	U31: {1}
8.29/3.03	U32: {1}
8.29/3.03	isQid: empty set
8.29/3.03	U41: {1}
8.29/3.03	U42: {1}
8.29/3.03	U43: {1}
8.29/3.03	U51: {1}
8.29/3.03	U52: {1}
8.29/3.03	U53: {1}
8.29/3.03	U61: {1}
8.29/3.03	U62: {1}
8.29/3.03	U71: {1}
8.29/3.03	U72: {1}
8.29/3.03	isNePal: empty set
8.29/3.03	and: {1}
8.29/3.03	isPalListKind: empty set
8.29/3.03	isPal: empty set
8.29/3.03	a: empty set
8.29/3.03	e: empty set
8.29/3.03	i: empty set
8.29/3.03	o: empty set
8.29/3.03	u: empty set
8.29/3.03	Used ordering:
8.29/3.03	Polynomial interpretation [POLO]:
8.29/3.03	
8.29/3.03	   POL(U11(x_1, x_2)) = x_1
8.29/3.03	   POL(U12(x_1)) = x_1
8.29/3.03	   POL(U21(x_1, x_2, x_3)) = x_1
8.29/3.03	   POL(U22(x_1, x_2)) = 2*x_1
8.29/3.03	   POL(U23(x_1)) = 2*x_1
8.29/3.03	   POL(U31(x_1, x_2)) = 2*x_1
8.29/3.03	   POL(U32(x_1)) = 2*x_1
8.29/3.03	   POL(U41(x_1, x_2, x_3)) = x_1
8.29/3.03	   POL(U42(x_1, x_2)) = 2*x_1
8.29/3.03	   POL(U43(x_1)) = 2*x_1
8.29/3.03	   POL(U51(x_1, x_2, x_3)) = x_1
8.29/3.03	   POL(U52(x_1, x_2)) = 2*x_1
8.29/3.03	   POL(U53(x_1)) = 2*x_1
8.29/3.03	   POL(U61(x_1, x_2)) = 2*x_1
8.29/3.03	   POL(U62(x_1)) = 2*x_1
8.29/3.03	   POL(U71(x_1, x_2)) = 2*x_1
8.29/3.03	   POL(U72(x_1)) = 2*x_1
8.29/3.03	   POL(__(x_1, x_2)) = x_1 + x_2
8.29/3.03	   POL(a) = 0
8.29/3.03	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.03	   POL(e) = 0
8.29/3.03	   POL(i) = 0
8.29/3.03	   POL(isList(x_1)) = 0
8.29/3.03	   POL(isNeList(x_1)) = 0
8.29/3.03	   POL(isNePal(x_1)) = 0
8.29/3.03	   POL(isPal(x_1)) = 0
8.29/3.03	   POL(isPalListKind(x_1)) = 0
8.29/3.03	   POL(isQid(x_1)) = 0
8.29/3.03	   POL(nil) = 1
8.29/3.03	   POL(o) = 0
8.29/3.03	   POL(tt) = 0
8.29/3.03	   POL(u) = 0
8.29/3.03	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.03	
8.29/3.03	   __(X, nil) -> X
8.29/3.03	   __(nil, X) -> X
8.29/3.03	
8.29/3.03	
8.29/3.03	
8.29/3.03	
8.29/3.03	----------------------------------------
8.29/3.03	
8.29/3.03	(4)
8.29/3.03	Obligation:
8.29/3.03	Context-sensitive rewrite system:
8.29/3.03	The TRS R consists of the following rules:
8.29/3.03	
8.29/3.03	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.03	   U11(tt, V) -> U12(isNeList(V))
8.29/3.03	   U12(tt) -> tt
8.29/3.03	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.03	   U22(tt, V2) -> U23(isList(V2))
8.29/3.03	   U23(tt) -> tt
8.29/3.03	   U31(tt, V) -> U32(isQid(V))
8.29/3.03	   U32(tt) -> tt
8.29/3.03	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.03	   U42(tt, V2) -> U43(isNeList(V2))
8.29/3.03	   U43(tt) -> tt
8.29/3.03	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.03	   U52(tt, V2) -> U53(isList(V2))
8.29/3.03	   U53(tt) -> tt
8.29/3.03	   U61(tt, V) -> U62(isQid(V))
8.29/3.03	   U62(tt) -> tt
8.29/3.03	   U71(tt, V) -> U72(isNePal(V))
8.29/3.03	   U72(tt) -> tt
8.29/3.03	   and(tt, X) -> X
8.29/3.03	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.03	   isList(nil) -> tt
8.29/3.03	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.03	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.03	   isNePal(__(I, __(P, I))) -> and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))
8.29/3.03	   isPal(V) -> U71(isPalListKind(V), V)
8.29/3.03	   isPal(nil) -> tt
8.29/3.03	   isPalListKind(a) -> tt
8.29/3.03	   isPalListKind(e) -> tt
8.29/3.03	   isPalListKind(i) -> tt
8.29/3.03	   isPalListKind(nil) -> tt
8.29/3.03	   isPalListKind(o) -> tt
8.29/3.03	   isPalListKind(u) -> tt
8.29/3.03	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.03	   isQid(a) -> tt
8.29/3.03	   isQid(e) -> tt
8.29/3.03	   isQid(i) -> tt
8.29/3.03	   isQid(o) -> tt
8.29/3.03	   isQid(u) -> tt
8.29/3.03	
8.29/3.03	The replacement map contains the following entries:
8.29/3.03	
8.29/3.03	__: {1, 2}
8.29/3.03	nil: empty set
8.29/3.03	U11: {1}
8.29/3.03	tt: empty set
8.29/3.03	U12: {1}
8.29/3.03	isNeList: empty set
8.29/3.03	U21: {1}
8.29/3.03	U22: {1}
8.29/3.03	isList: empty set
8.29/3.03	U23: {1}
8.29/3.03	U31: {1}
8.29/3.03	U32: {1}
8.29/3.03	isQid: empty set
8.29/3.03	U41: {1}
8.29/3.03	U42: {1}
8.29/3.03	U43: {1}
8.29/3.03	U51: {1}
8.29/3.03	U52: {1}
8.29/3.03	U53: {1}
8.29/3.03	U61: {1}
8.29/3.03	U62: {1}
8.29/3.03	U71: {1}
8.29/3.03	U72: {1}
8.29/3.03	isNePal: empty set
8.29/3.03	and: {1}
8.29/3.03	isPalListKind: empty set
8.29/3.03	isPal: empty set
8.29/3.03	a: empty set
8.29/3.03	e: empty set
8.29/3.03	i: empty set
8.29/3.03	o: empty set
8.29/3.03	u: empty set
8.29/3.03	
8.29/3.03	----------------------------------------
8.29/3.03	
8.29/3.03	(5) CSRRRRProof (EQUIVALENT)
8.29/3.03	The following CSR is given: Context-sensitive rewrite system:
8.29/3.03	The TRS R consists of the following rules:
8.29/3.03	
8.29/3.03	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.03	   U11(tt, V) -> U12(isNeList(V))
8.29/3.03	   U12(tt) -> tt
8.29/3.03	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.03	   U22(tt, V2) -> U23(isList(V2))
8.29/3.03	   U23(tt) -> tt
8.29/3.03	   U31(tt, V) -> U32(isQid(V))
8.29/3.03	   U32(tt) -> tt
8.29/3.03	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.03	   U42(tt, V2) -> U43(isNeList(V2))
8.29/3.03	   U43(tt) -> tt
8.29/3.03	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.03	   U52(tt, V2) -> U53(isList(V2))
8.29/3.03	   U53(tt) -> tt
8.29/3.03	   U61(tt, V) -> U62(isQid(V))
8.29/3.03	   U62(tt) -> tt
8.29/3.03	   U71(tt, V) -> U72(isNePal(V))
8.29/3.03	   U72(tt) -> tt
8.29/3.03	   and(tt, X) -> X
8.29/3.03	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.03	   isList(nil) -> tt
8.29/3.03	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.03	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.03	   isNePal(__(I, __(P, I))) -> and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))
8.29/3.03	   isPal(V) -> U71(isPalListKind(V), V)
8.29/3.03	   isPal(nil) -> tt
8.29/3.03	   isPalListKind(a) -> tt
8.29/3.03	   isPalListKind(e) -> tt
8.29/3.03	   isPalListKind(i) -> tt
8.29/3.03	   isPalListKind(nil) -> tt
8.29/3.03	   isPalListKind(o) -> tt
8.29/3.03	   isPalListKind(u) -> tt
8.29/3.03	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.03	   isQid(a) -> tt
8.29/3.03	   isQid(e) -> tt
8.29/3.03	   isQid(i) -> tt
8.29/3.03	   isQid(o) -> tt
8.29/3.03	   isQid(u) -> tt
8.29/3.03	
8.29/3.03	The replacement map contains the following entries:
8.29/3.03	
8.29/3.03	__: {1, 2}
8.29/3.03	nil: empty set
8.29/3.03	U11: {1}
8.29/3.03	tt: empty set
8.29/3.03	U12: {1}
8.29/3.03	isNeList: empty set
8.29/3.03	U21: {1}
8.29/3.03	U22: {1}
8.29/3.03	isList: empty set
8.29/3.03	U23: {1}
8.29/3.03	U31: {1}
8.29/3.03	U32: {1}
8.29/3.03	isQid: empty set
8.29/3.03	U41: {1}
8.29/3.03	U42: {1}
8.29/3.03	U43: {1}
8.29/3.03	U51: {1}
8.29/3.03	U52: {1}
8.29/3.03	U53: {1}
8.29/3.03	U61: {1}
8.29/3.03	U62: {1}
8.29/3.03	U71: {1}
8.29/3.03	U72: {1}
8.29/3.03	isNePal: empty set
8.29/3.03	and: {1}
8.29/3.03	isPalListKind: empty set
8.29/3.03	isPal: empty set
8.29/3.03	a: empty set
8.29/3.03	e: empty set
8.29/3.03	i: empty set
8.29/3.03	o: empty set
8.29/3.03	u: empty set
8.29/3.03	Used ordering:
8.29/3.03	Polynomial interpretation [POLO]:
8.29/3.03	
8.29/3.03	   POL(U11(x_1, x_2)) = x_1 + x_2
8.29/3.03	   POL(U12(x_1)) = x_1
8.29/3.03	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.03	   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.03	   POL(U23(x_1)) = 1 + x_1
8.29/3.03	   POL(U31(x_1, x_2)) = x_1 + x_2
8.29/3.03	   POL(U32(x_1)) = x_1
8.29/3.03	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.03	   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.03	   POL(U43(x_1)) = 1 + x_1
8.29/3.03	   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.03	   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.03	   POL(U53(x_1)) = 1 + x_1
8.29/3.03	   POL(U61(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.03	   POL(U62(x_1)) = 1 + x_1
8.29/3.03	   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.03	   POL(U72(x_1)) = x_1
8.29/3.03	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.03	   POL(a) = 0
8.29/3.03	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.03	   POL(e) = 0
8.29/3.03	   POL(i) = 1
8.29/3.03	   POL(isList(x_1)) = x_1
8.29/3.03	   POL(isNeList(x_1)) = x_1
8.29/3.03	   POL(isNePal(x_1)) = 1 + x_1
8.29/3.03	   POL(isPal(x_1)) = 1 + x_1
8.29/3.03	   POL(isPalListKind(x_1)) = 0
8.29/3.03	   POL(isQid(x_1)) = x_1
8.29/3.03	   POL(nil) = 1
8.29/3.03	   POL(o) = 1
8.29/3.03	   POL(tt) = 0
8.29/3.03	   POL(u) = 1
8.29/3.03	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.03	
8.29/3.03	   U23(tt) -> tt
8.29/3.03	   U43(tt) -> tt
8.29/3.03	   U53(tt) -> tt
8.29/3.03	   U62(tt) -> tt
8.29/3.03	   isList(nil) -> tt
8.29/3.03	   isNePal(__(I, __(P, I))) -> and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))
8.29/3.03	   isPal(nil) -> tt
8.29/3.03	   isQid(i) -> tt
8.29/3.03	   isQid(o) -> tt
8.29/3.03	   isQid(u) -> tt
8.29/3.03	
8.29/3.03	
8.29/3.03	
8.29/3.03	
8.29/3.03	----------------------------------------
8.29/3.03	
8.29/3.03	(6)
8.29/3.03	Obligation:
8.29/3.03	Context-sensitive rewrite system:
8.29/3.03	The TRS R consists of the following rules:
8.29/3.03	
8.29/3.03	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.03	   U11(tt, V) -> U12(isNeList(V))
8.29/3.03	   U12(tt) -> tt
8.29/3.03	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.03	   U22(tt, V2) -> U23(isList(V2))
8.29/3.03	   U31(tt, V) -> U32(isQid(V))
8.29/3.03	   U32(tt) -> tt
8.29/3.03	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.03	   U42(tt, V2) -> U43(isNeList(V2))
8.29/3.03	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.03	   U52(tt, V2) -> U53(isList(V2))
8.29/3.03	   U61(tt, V) -> U62(isQid(V))
8.29/3.03	   U71(tt, V) -> U72(isNePal(V))
8.29/3.03	   U72(tt) -> tt
8.29/3.03	   and(tt, X) -> X
8.29/3.03	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.03	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.03	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.03	   isPal(V) -> U71(isPalListKind(V), V)
8.29/3.03	   isPalListKind(a) -> tt
8.29/3.03	   isPalListKind(e) -> tt
8.29/3.03	   isPalListKind(i) -> tt
8.29/3.03	   isPalListKind(nil) -> tt
8.29/3.03	   isPalListKind(o) -> tt
8.29/3.03	   isPalListKind(u) -> tt
8.29/3.03	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.03	   isQid(a) -> tt
8.29/3.03	   isQid(e) -> tt
8.29/3.03	
8.29/3.03	The replacement map contains the following entries:
8.29/3.03	
8.29/3.03	__: {1, 2}
8.29/3.03	nil: empty set
8.29/3.03	U11: {1}
8.29/3.03	tt: empty set
8.29/3.03	U12: {1}
8.29/3.03	isNeList: empty set
8.29/3.03	U21: {1}
8.29/3.03	U22: {1}
8.29/3.03	isList: empty set
8.29/3.03	U23: {1}
8.29/3.03	U31: {1}
8.29/3.03	U32: {1}
8.29/3.03	isQid: empty set
8.29/3.03	U41: {1}
8.29/3.03	U42: {1}
8.29/3.03	U43: {1}
8.29/3.03	U51: {1}
8.29/3.03	U52: {1}
8.29/3.03	U53: {1}
8.29/3.03	U61: {1}
8.29/3.03	U62: {1}
8.29/3.03	U71: {1}
8.29/3.03	U72: {1}
8.29/3.03	isNePal: empty set
8.29/3.03	and: {1}
8.29/3.03	isPalListKind: empty set
8.29/3.03	isPal: empty set
8.29/3.03	a: empty set
8.29/3.03	e: empty set
8.29/3.03	i: empty set
8.29/3.03	o: empty set
8.29/3.03	u: empty set
8.29/3.03	
8.29/3.03	----------------------------------------
8.29/3.03	
8.29/3.03	(7) CSRRRRProof (EQUIVALENT)
8.29/3.03	The following CSR is given: Context-sensitive rewrite system:
8.29/3.03	The TRS R consists of the following rules:
8.29/3.03	
8.29/3.03	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.03	   U11(tt, V) -> U12(isNeList(V))
8.29/3.03	   U12(tt) -> tt
8.29/3.03	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.03	   U22(tt, V2) -> U23(isList(V2))
8.29/3.03	   U31(tt, V) -> U32(isQid(V))
8.29/3.03	   U32(tt) -> tt
8.29/3.03	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.03	   U42(tt, V2) -> U43(isNeList(V2))
8.29/3.03	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.03	   U52(tt, V2) -> U53(isList(V2))
8.29/3.03	   U61(tt, V) -> U62(isQid(V))
8.29/3.03	   U71(tt, V) -> U72(isNePal(V))
8.29/3.03	   U72(tt) -> tt
8.29/3.03	   and(tt, X) -> X
8.29/3.03	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.03	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.03	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.03	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.03	   isPal(V) -> U71(isPalListKind(V), V)
8.29/3.03	   isPalListKind(a) -> tt
8.29/3.03	   isPalListKind(e) -> tt
8.29/3.03	   isPalListKind(i) -> tt
8.29/3.03	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	   isQid(a) -> tt
8.29/3.04	   isQid(e) -> tt
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U43: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U53: {1}
8.29/3.04	U61: {1}
8.29/3.04	U62: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	isPal: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	Used ordering:
8.29/3.04	Polynomial interpretation [POLO]:
8.29/3.04	
8.29/3.04	   POL(U11(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U12(x_1)) = x_1
8.29/3.04	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U23(x_1)) = 1 + x_1
8.29/3.04	   POL(U31(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U32(x_1)) = x_1
8.29/3.04	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U43(x_1)) = 1 + x_1
8.29/3.04	   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U53(x_1)) = 1 + x_1
8.29/3.04	   POL(U61(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U62(x_1)) = 1 + x_1
8.29/3.04	   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U72(x_1)) = x_1
8.29/3.04	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(a) = 0
8.29/3.04	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(e) = 1
8.29/3.04	   POL(i) = 1
8.29/3.04	   POL(isList(x_1)) = x_1
8.29/3.04	   POL(isNeList(x_1)) = x_1
8.29/3.04	   POL(isNePal(x_1)) = 1 + x_1
8.29/3.04	   POL(isPal(x_1)) = 1 + x_1
8.29/3.04	   POL(isPalListKind(x_1)) = 0
8.29/3.04	   POL(isQid(x_1)) = x_1
8.29/3.04	   POL(nil) = 1
8.29/3.04	   POL(o) = 1
8.29/3.04	   POL(tt) = 0
8.29/3.04	   POL(u) = 1
8.29/3.04	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.04	
8.29/3.04	   isQid(e) -> tt
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(8)
8.29/3.04	Obligation:
8.29/3.04	Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U42(tt, V2) -> U43(isNeList(V2))
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U52(tt, V2) -> U53(isList(V2))
8.29/3.04	   U61(tt, V) -> U62(isQid(V))
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPal(V) -> U71(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	   isQid(a) -> tt
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U43: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U53: {1}
8.29/3.04	U61: {1}
8.29/3.04	U62: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	isPal: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(9) CSRRRRProof (EQUIVALENT)
8.29/3.04	The following CSR is given: Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U42(tt, V2) -> U43(isNeList(V2))
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U52(tt, V2) -> U53(isList(V2))
8.29/3.04	   U61(tt, V) -> U62(isQid(V))
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPal(V) -> U71(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	   isQid(a) -> tt
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U43: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U53: {1}
8.29/3.04	U61: {1}
8.29/3.04	U62: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	isPal: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	Used ordering:
8.29/3.04	Polynomial interpretation [POLO]:
8.29/3.04	
8.29/3.04	   POL(U11(x_1, x_2)) = 2*x_1
8.29/3.04	   POL(U12(x_1)) = 2*x_1
8.29/3.04	   POL(U21(x_1, x_2, x_3)) = x_1
8.29/3.04	   POL(U22(x_1, x_2)) = x_1
8.29/3.04	   POL(U23(x_1)) = 2*x_1
8.29/3.04	   POL(U31(x_1, x_2)) = x_1
8.29/3.04	   POL(U32(x_1)) = x_1
8.29/3.04	   POL(U41(x_1, x_2, x_3)) = 2*x_1
8.29/3.04	   POL(U42(x_1, x_2)) = x_1
8.29/3.04	   POL(U43(x_1)) = 2*x_1
8.29/3.04	   POL(U51(x_1, x_2, x_3)) = 2*x_1
8.29/3.04	   POL(U52(x_1, x_2)) = 2*x_1
8.29/3.04	   POL(U53(x_1)) = 2*x_1
8.29/3.04	   POL(U61(x_1, x_2)) = x_1
8.29/3.04	   POL(U62(x_1)) = x_1
8.29/3.04	   POL(U71(x_1, x_2)) = x_1 + 2*x_2
8.29/3.04	   POL(U72(x_1)) = 2*x_1
8.29/3.04	   POL(__(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(a) = 0
8.29/3.04	   POL(and(x_1, x_2)) = 2*x_1 + 2*x_2
8.29/3.04	   POL(e) = 2
8.29/3.04	   POL(i) = 2
8.29/3.04	   POL(isList(x_1)) = 0
8.29/3.04	   POL(isNeList(x_1)) = 0
8.29/3.04	   POL(isNePal(x_1)) = 0
8.29/3.04	   POL(isPal(x_1)) = 1 + 2*x_1
8.29/3.04	   POL(isPalListKind(x_1)) = 0
8.29/3.04	   POL(isQid(x_1)) = 0
8.29/3.04	   POL(nil) = 2
8.29/3.04	   POL(o) = 2
8.29/3.04	   POL(tt) = 0
8.29/3.04	   POL(u) = 2
8.29/3.04	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.04	
8.29/3.04	   isPal(V) -> U71(isPalListKind(V), V)
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(10)
8.29/3.04	Obligation:
8.29/3.04	Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U42(tt, V2) -> U43(isNeList(V2))
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U52(tt, V2) -> U53(isList(V2))
8.29/3.04	   U61(tt, V) -> U62(isQid(V))
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	   isQid(a) -> tt
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U43: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U53: {1}
8.29/3.04	U61: {1}
8.29/3.04	U62: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(11) CSRRRRProof (EQUIVALENT)
8.29/3.04	The following CSR is given: Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U42(tt, V2) -> U43(isNeList(V2))
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U52(tt, V2) -> U53(isList(V2))
8.29/3.04	   U61(tt, V) -> U62(isQid(V))
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	   isQid(a) -> tt
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U43: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U53: {1}
8.29/3.04	U61: {1}
8.29/3.04	U62: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	Used ordering:
8.29/3.04	Polynomial interpretation [POLO]:
8.29/3.04	
8.29/3.04	   POL(U11(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U12(x_1)) = x_1
8.29/3.04	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U23(x_1)) = 1 + x_1
8.29/3.04	   POL(U31(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U32(x_1)) = x_1
8.29/3.04	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U43(x_1)) = x_1
8.29/3.04	   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U53(x_1)) = 1 + x_1
8.29/3.04	   POL(U61(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U62(x_1)) = 1 + x_1
8.29/3.04	   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U72(x_1)) = x_1
8.29/3.04	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(a) = 0
8.29/3.04	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(e) = 1
8.29/3.04	   POL(i) = 1
8.29/3.04	   POL(isList(x_1)) = x_1
8.29/3.04	   POL(isNeList(x_1)) = x_1
8.29/3.04	   POL(isNePal(x_1)) = 1 + x_1
8.29/3.04	   POL(isPalListKind(x_1)) = 0
8.29/3.04	   POL(isQid(x_1)) = x_1
8.29/3.04	   POL(nil) = 1
8.29/3.04	   POL(o) = 1
8.29/3.04	   POL(tt) = 0
8.29/3.04	   POL(u) = 1
8.29/3.04	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.04	
8.29/3.04	   U42(tt, V2) -> U43(isNeList(V2))
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(12)
8.29/3.04	Obligation:
8.29/3.04	Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U52(tt, V2) -> U53(isList(V2))
8.29/3.04	   U61(tt, V) -> U62(isQid(V))
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	   isQid(a) -> tt
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U53: {1}
8.29/3.04	U61: {1}
8.29/3.04	U62: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(13) CSRRRRProof (EQUIVALENT)
8.29/3.04	The following CSR is given: Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U52(tt, V2) -> U53(isList(V2))
8.29/3.04	   U61(tt, V) -> U62(isQid(V))
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	   isQid(a) -> tt
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U53: {1}
8.29/3.04	U61: {1}
8.29/3.04	U62: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	Used ordering:
8.29/3.04	Polynomial interpretation [POLO]:
8.29/3.04	
8.29/3.04	   POL(U11(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U12(x_1)) = x_1
8.29/3.04	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U23(x_1)) = 1 + x_1
8.29/3.04	   POL(U31(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U32(x_1)) = x_1
8.29/3.04	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U53(x_1)) = 1 + x_1
8.29/3.04	   POL(U61(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U62(x_1)) = 1 + x_1
8.29/3.04	   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U72(x_1)) = x_1
8.29/3.04	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(a) = 1
8.29/3.04	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(e) = 1
8.29/3.04	   POL(i) = 1
8.29/3.04	   POL(isList(x_1)) = x_1
8.29/3.04	   POL(isNeList(x_1)) = x_1
8.29/3.04	   POL(isNePal(x_1)) = 1 + x_1
8.29/3.04	   POL(isPalListKind(x_1)) = 0
8.29/3.04	   POL(isQid(x_1)) = x_1
8.29/3.04	   POL(nil) = 1
8.29/3.04	   POL(o) = 1
8.29/3.04	   POL(tt) = 0
8.29/3.04	   POL(u) = 1
8.29/3.04	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.04	
8.29/3.04	   isQid(a) -> tt
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(14)
8.29/3.04	Obligation:
8.29/3.04	Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U52(tt, V2) -> U53(isList(V2))
8.29/3.04	   U61(tt, V) -> U62(isQid(V))
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U53: {1}
8.29/3.04	U61: {1}
8.29/3.04	U62: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(15) CSRRRRProof (EQUIVALENT)
8.29/3.04	The following CSR is given: Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U52(tt, V2) -> U53(isList(V2))
8.29/3.04	   U61(tt, V) -> U62(isQid(V))
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U53: {1}
8.29/3.04	U61: {1}
8.29/3.04	U62: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	Used ordering:
8.29/3.04	Polynomial interpretation [POLO]:
8.29/3.04	
8.29/3.04	   POL(U11(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U12(x_1)) = x_1
8.29/3.04	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U23(x_1)) = 1 + x_1
8.29/3.04	   POL(U31(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U32(x_1)) = x_1
8.29/3.04	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U53(x_1)) = x_1
8.29/3.04	   POL(U61(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U62(x_1)) = 1 + x_1
8.29/3.04	   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U72(x_1)) = x_1
8.29/3.04	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(a) = 1
8.29/3.04	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(e) = 1
8.29/3.04	   POL(i) = 1
8.29/3.04	   POL(isList(x_1)) = x_1
8.29/3.04	   POL(isNeList(x_1)) = x_1
8.29/3.04	   POL(isNePal(x_1)) = 1 + x_1
8.29/3.04	   POL(isPalListKind(x_1)) = 0
8.29/3.04	   POL(isQid(x_1)) = x_1
8.29/3.04	   POL(nil) = 1
8.29/3.04	   POL(o) = 1
8.29/3.04	   POL(tt) = 0
8.29/3.04	   POL(u) = 1
8.29/3.04	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.04	
8.29/3.04	   U52(tt, V2) -> U53(isList(V2))
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(16)
8.29/3.04	Obligation:
8.29/3.04	Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U61(tt, V) -> U62(isQid(V))
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U61: {1}
8.29/3.04	U62: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(17) CSRRRRProof (EQUIVALENT)
8.29/3.04	The following CSR is given: Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U61(tt, V) -> U62(isQid(V))
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U61: {1}
8.29/3.04	U62: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	Used ordering:
8.29/3.04	Polynomial interpretation [POLO]:
8.29/3.04	
8.29/3.04	   POL(U11(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U12(x_1)) = x_1
8.29/3.04	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U23(x_1)) = 1 + x_1
8.29/3.04	   POL(U31(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U32(x_1)) = x_1
8.29/3.04	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U61(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U62(x_1)) = x_1
8.29/3.04	   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U72(x_1)) = x_1
8.29/3.04	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(a) = 1
8.29/3.04	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(e) = 1
8.29/3.04	   POL(i) = 1
8.29/3.04	   POL(isList(x_1)) = x_1
8.29/3.04	   POL(isNeList(x_1)) = x_1
8.29/3.04	   POL(isNePal(x_1)) = 1 + x_1
8.29/3.04	   POL(isPalListKind(x_1)) = 0
8.29/3.04	   POL(isQid(x_1)) = x_1
8.29/3.04	   POL(nil) = 1
8.29/3.04	   POL(o) = 1
8.29/3.04	   POL(tt) = 0
8.29/3.04	   POL(u) = 1
8.29/3.04	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.04	
8.29/3.04	   U61(tt, V) -> U62(isQid(V))
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(18)
8.29/3.04	Obligation:
8.29/3.04	Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U61: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(19) CSRRRRProof (EQUIVALENT)
8.29/3.04	The following CSR is given: Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U61: {1}
8.29/3.04	U71: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	Used ordering:
8.29/3.04	Polynomial interpretation [POLO]:
8.29/3.04	
8.29/3.04	   POL(U11(x_1, x_2)) = x_1
8.29/3.04	   POL(U12(x_1)) = x_1
8.29/3.04	   POL(U21(x_1, x_2, x_3)) = 2*x_1
8.29/3.04	   POL(U22(x_1, x_2)) = x_1
8.29/3.04	   POL(U23(x_1)) = 2*x_1
8.29/3.04	   POL(U31(x_1, x_2)) = 2*x_1
8.29/3.04	   POL(U32(x_1)) = x_1
8.29/3.04	   POL(U41(x_1, x_2, x_3)) = 2*x_1
8.29/3.04	   POL(U42(x_1, x_2)) = 2*x_1
8.29/3.04	   POL(U51(x_1, x_2, x_3)) = 2*x_1
8.29/3.04	   POL(U52(x_1, x_2)) = 2*x_1
8.29/3.04	   POL(U61(x_1, x_2)) = 2*x_1 + x_2
8.29/3.04	   POL(U71(x_1, x_2)) = 2 + x_1 + 2*x_2
8.29/3.04	   POL(U72(x_1)) = 2*x_1
8.29/3.04	   POL(__(x_1, x_2)) = 2 + 2*x_1 + x_2
8.29/3.04	   POL(a) = 2
8.29/3.04	   POL(and(x_1, x_2)) = x_1 + 2*x_2
8.29/3.04	   POL(e) = 2
8.29/3.04	   POL(i) = 2
8.29/3.04	   POL(isList(x_1)) = 0
8.29/3.04	   POL(isNeList(x_1)) = 0
8.29/3.04	   POL(isNePal(x_1)) = x_1
8.29/3.04	   POL(isPalListKind(x_1)) = 0
8.29/3.04	   POL(isQid(x_1)) = 0
8.29/3.04	   POL(nil) = 2
8.29/3.04	   POL(o) = 2
8.29/3.04	   POL(tt) = 0
8.29/3.04	   POL(u) = 2
8.29/3.04	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.04	
8.29/3.04	   __(__(X, Y), Z) -> __(X, __(Y, Z))
8.29/3.04	   U71(tt, V) -> U72(isNePal(V))
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(20)
8.29/3.04	Obligation:
8.29/3.04	Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U61: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(21) CSRRRRProof (EQUIVALENT)
8.29/3.04	The following CSR is given: Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   U72(tt) -> tt
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U61: {1}
8.29/3.04	U72: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	Used ordering:
8.29/3.04	Polynomial interpretation [POLO]:
8.29/3.04	
8.29/3.04	   POL(U11(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U12(x_1)) = x_1
8.29/3.04	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U23(x_1)) = 1 + x_1
8.29/3.04	   POL(U31(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U32(x_1)) = x_1
8.29/3.04	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U61(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U72(x_1)) = 1 + x_1
8.29/3.04	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(a) = 1
8.29/3.04	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(e) = 1
8.29/3.04	   POL(i) = 1
8.29/3.04	   POL(isList(x_1)) = x_1
8.29/3.04	   POL(isNeList(x_1)) = x_1
8.29/3.04	   POL(isNePal(x_1)) = 1 + x_1
8.29/3.04	   POL(isPalListKind(x_1)) = 0
8.29/3.04	   POL(isQid(x_1)) = x_1
8.29/3.04	   POL(nil) = 1
8.29/3.04	   POL(o) = 1
8.29/3.04	   POL(tt) = 0
8.29/3.04	   POL(u) = 1
8.29/3.04	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.04	
8.29/3.04	   U72(tt) -> tt
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(22)
8.29/3.04	Obligation:
8.29/3.04	Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U61: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	
8.29/3.04	----------------------------------------
8.29/3.04	
8.29/3.04	(23) CSRRRRProof (EQUIVALENT)
8.29/3.04	The following CSR is given: Context-sensitive rewrite system:
8.29/3.04	The TRS R consists of the following rules:
8.29/3.04	
8.29/3.04	   U11(tt, V) -> U12(isNeList(V))
8.29/3.04	   U12(tt) -> tt
8.29/3.04	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.04	   U22(tt, V2) -> U23(isList(V2))
8.29/3.04	   U31(tt, V) -> U32(isQid(V))
8.29/3.04	   U32(tt) -> tt
8.29/3.04	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.04	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.04	   and(tt, X) -> X
8.29/3.04	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.04	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.04	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.04	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.04	   isPalListKind(a) -> tt
8.29/3.04	   isPalListKind(e) -> tt
8.29/3.04	   isPalListKind(i) -> tt
8.29/3.04	   isPalListKind(nil) -> tt
8.29/3.04	   isPalListKind(o) -> tt
8.29/3.04	   isPalListKind(u) -> tt
8.29/3.04	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.04	
8.29/3.04	The replacement map contains the following entries:
8.29/3.04	
8.29/3.04	__: {1, 2}
8.29/3.04	nil: empty set
8.29/3.04	U11: {1}
8.29/3.04	tt: empty set
8.29/3.04	U12: {1}
8.29/3.04	isNeList: empty set
8.29/3.04	U21: {1}
8.29/3.04	U22: {1}
8.29/3.04	isList: empty set
8.29/3.04	U23: {1}
8.29/3.04	U31: {1}
8.29/3.04	U32: {1}
8.29/3.04	isQid: empty set
8.29/3.04	U41: {1}
8.29/3.04	U42: {1}
8.29/3.04	U51: {1}
8.29/3.04	U52: {1}
8.29/3.04	U61: {1}
8.29/3.04	isNePal: empty set
8.29/3.04	and: {1}
8.29/3.04	isPalListKind: empty set
8.29/3.04	a: empty set
8.29/3.04	e: empty set
8.29/3.04	i: empty set
8.29/3.04	o: empty set
8.29/3.04	u: empty set
8.29/3.04	Used ordering:
8.29/3.04	Polynomial interpretation [POLO]:
8.29/3.04	
8.29/3.04	   POL(U11(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U12(x_1)) = x_1
8.29/3.04	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U23(x_1)) = 1 + x_1
8.29/3.04	   POL(U31(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(U32(x_1)) = x_1
8.29/3.04	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.04	   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(U61(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.04	   POL(a) = 1
8.29/3.04	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.04	   POL(e) = 1
8.29/3.04	   POL(i) = 1
8.29/3.04	   POL(isList(x_1)) = x_1
8.29/3.04	   POL(isNeList(x_1)) = x_1
8.29/3.05	   POL(isNePal(x_1)) = 1 + x_1
8.29/3.05	   POL(isPalListKind(x_1)) = 0
8.29/3.05	   POL(isQid(x_1)) = x_1
8.29/3.05	   POL(nil) = 1
8.29/3.05	   POL(o) = 1
8.29/3.05	   POL(tt) = 0
8.29/3.05	   POL(u) = 1
8.29/3.05	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.05	
8.29/3.05	   isNePal(V) -> U61(isPalListKind(V), V)
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(24)
8.29/3.05	Obligation:
8.29/3.05	Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U22(tt, V2) -> U23(isList(V2))
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	   U32(tt) -> tt
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U23: {1}
8.29/3.05	U31: {1}
8.29/3.05	U32: {1}
8.29/3.05	isQid: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	U51: {1}
8.29/3.05	U52: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(25) CSRRRRProof (EQUIVALENT)
8.29/3.05	The following CSR is given: Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U22(tt, V2) -> U23(isList(V2))
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	   U32(tt) -> tt
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U23: {1}
8.29/3.05	U31: {1}
8.29/3.05	U32: {1}
8.29/3.05	isQid: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	U51: {1}
8.29/3.05	U52: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	Used ordering:
8.29/3.05	Polynomial interpretation [POLO]:
8.29/3.05	
8.29/3.05	   POL(U11(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(U12(x_1)) = x_1
8.29/3.05	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(U23(x_1)) = 1 + x_1
8.29/3.05	   POL(U31(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(U32(x_1)) = x_1
8.29/3.05	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U52(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(a) = 1
8.29/3.05	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(e) = 1
8.29/3.05	   POL(i) = 1
8.29/3.05	   POL(isList(x_1)) = x_1
8.29/3.05	   POL(isNeList(x_1)) = x_1
8.29/3.05	   POL(isPalListKind(x_1)) = 0
8.29/3.05	   POL(isQid(x_1)) = x_1
8.29/3.05	   POL(nil) = 1
8.29/3.05	   POL(o) = 1
8.29/3.05	   POL(tt) = 0
8.29/3.05	   POL(u) = 1
8.29/3.05	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.05	
8.29/3.05	   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(26)
8.29/3.05	Obligation:
8.29/3.05	Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U22(tt, V2) -> U23(isList(V2))
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	   U32(tt) -> tt
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U23: {1}
8.29/3.05	U31: {1}
8.29/3.05	U32: {1}
8.29/3.05	isQid: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	U51: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(27) CSRRRRProof (EQUIVALENT)
8.29/3.05	The following CSR is given: Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U22(tt, V2) -> U23(isList(V2))
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	   U32(tt) -> tt
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U23: {1}
8.29/3.05	U31: {1}
8.29/3.05	U32: {1}
8.29/3.05	isQid: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	U51: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	Used ordering:
8.29/3.05	Polynomial interpretation [POLO]:
8.29/3.05	
8.29/3.05	   POL(U11(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(U12(x_1)) = x_1
8.29/3.05	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(U23(x_1)) = x_1
8.29/3.05	   POL(U31(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(U32(x_1)) = x_1
8.29/3.05	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(a) = 1
8.29/3.05	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(e) = 1
8.29/3.05	   POL(i) = 1
8.29/3.05	   POL(isList(x_1)) = x_1
8.29/3.05	   POL(isNeList(x_1)) = x_1
8.29/3.05	   POL(isPalListKind(x_1)) = 0
8.29/3.05	   POL(isQid(x_1)) = x_1
8.29/3.05	   POL(nil) = 1
8.29/3.05	   POL(o) = 1
8.29/3.05	   POL(tt) = 0
8.29/3.05	   POL(u) = 1
8.29/3.05	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.05	
8.29/3.05	   U22(tt, V2) -> U23(isList(V2))
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(28)
8.29/3.05	Obligation:
8.29/3.05	Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	   U32(tt) -> tt
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U31: {1}
8.29/3.05	U32: {1}
8.29/3.05	isQid: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	U51: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(29) CSRRRRProof (EQUIVALENT)
8.29/3.05	The following CSR is given: Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	   U32(tt) -> tt
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U31: {1}
8.29/3.05	U32: {1}
8.29/3.05	isQid: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	U51: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	Used ordering:
8.29/3.05	Polynomial interpretation [POLO]:
8.29/3.05	
8.29/3.05	   POL(U11(x_1, x_2)) = 1 + x_1
8.29/3.05	   POL(U12(x_1)) = x_1
8.29/3.05	   POL(U21(x_1, x_2, x_3)) = 1 + x_1
8.29/3.05	   POL(U22(x_1, x_2)) = x_1
8.29/3.05	   POL(U31(x_1, x_2)) = 1 + x_1
8.29/3.05	   POL(U32(x_1)) = 1 + x_1
8.29/3.05	   POL(U41(x_1, x_2, x_3)) = 1 + x_1
8.29/3.05	   POL(U42(x_1, x_2)) = x_1
8.29/3.05	   POL(U51(x_1, x_2, x_3)) = 1 + x_1
8.29/3.05	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(a) = 1
8.29/3.05	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(e) = 1
8.29/3.05	   POL(i) = 1
8.29/3.05	   POL(isList(x_1)) = 1
8.29/3.05	   POL(isNeList(x_1)) = 1
8.29/3.05	   POL(isPalListKind(x_1)) = 0
8.29/3.05	   POL(isQid(x_1)) = 0
8.29/3.05	   POL(nil) = 1
8.29/3.05	   POL(o) = 1
8.29/3.05	   POL(tt) = 0
8.29/3.05	   POL(u) = 1
8.29/3.05	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.05	
8.29/3.05	   U32(tt) -> tt
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(30)
8.29/3.05	Obligation:
8.29/3.05	Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U31: {1}
8.29/3.05	U32: {1}
8.29/3.05	isQid: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	U51: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(31) CSRRRRProof (EQUIVALENT)
8.29/3.05	The following CSR is given: Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U31: {1}
8.29/3.05	U32: {1}
8.29/3.05	isQid: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	U51: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	Used ordering:
8.29/3.05	Polynomial interpretation [POLO]:
8.29/3.05	
8.29/3.05	   POL(U11(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(U12(x_1)) = x_1
8.29/3.05	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(U31(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(U32(x_1)) = x_1
8.29/3.05	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(U51(x_1, x_2, x_3)) = x_1 + x_2 + x_3
8.29/3.05	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(a) = 1
8.29/3.05	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(e) = 1
8.29/3.05	   POL(i) = 1
8.29/3.05	   POL(isList(x_1)) = x_1
8.29/3.05	   POL(isNeList(x_1)) = x_1
8.29/3.05	   POL(isPalListKind(x_1)) = 0
8.29/3.05	   POL(isQid(x_1)) = x_1
8.29/3.05	   POL(nil) = 1
8.29/3.05	   POL(o) = 1
8.29/3.05	   POL(tt) = 0
8.29/3.05	   POL(u) = 1
8.29/3.05	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.05	
8.29/3.05	   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(32)
8.29/3.05	Obligation:
8.29/3.05	Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U31: {1}
8.29/3.05	U32: {1}
8.29/3.05	isQid: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(33) CSRRRRProof (EQUIVALENT)
8.29/3.05	The following CSR is given: Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U31: {1}
8.29/3.05	U32: {1}
8.29/3.05	isQid: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	Used ordering:
8.29/3.05	Polynomial interpretation [POLO]:
8.29/3.05	
8.29/3.05	   POL(U11(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(U12(x_1)) = x_1
8.29/3.05	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U22(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(U31(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(U32(x_1)) = x_1
8.29/3.05	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U42(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(a) = 1
8.29/3.05	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(e) = 1
8.29/3.05	   POL(i) = 1
8.29/3.05	   POL(isList(x_1)) = 1 + x_1
8.29/3.05	   POL(isNeList(x_1)) = 1 + x_1
8.29/3.05	   POL(isPalListKind(x_1)) = 0
8.29/3.05	   POL(isQid(x_1)) = 1 + x_1
8.29/3.05	   POL(nil) = 1
8.29/3.05	   POL(o) = 1
8.29/3.05	   POL(tt) = 0
8.29/3.05	   POL(u) = 1
8.29/3.05	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.05	
8.29/3.05	   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(34)
8.29/3.05	Obligation:
8.29/3.05	Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U31: {1}
8.29/3.05	U32: {1}
8.29/3.05	isQid: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(35) CSRRRRProof (EQUIVALENT)
8.29/3.05	The following CSR is given: Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U31: {1}
8.29/3.05	U32: {1}
8.29/3.05	isQid: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	Used ordering:
8.29/3.05	Polynomial interpretation [POLO]:
8.29/3.05	
8.29/3.05	   POL(U11(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(U12(x_1)) = x_1
8.29/3.05	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U22(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(U31(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(U32(x_1)) = x_1
8.29/3.05	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U42(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(a) = 1
8.29/3.05	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(e) = 1
8.29/3.05	   POL(i) = 1
8.29/3.05	   POL(isList(x_1)) = 1 + x_1
8.29/3.05	   POL(isNeList(x_1)) = 1 + x_1
8.29/3.05	   POL(isPalListKind(x_1)) = 0
8.29/3.05	   POL(isQid(x_1)) = x_1
8.29/3.05	   POL(nil) = 1
8.29/3.05	   POL(o) = 1
8.29/3.05	   POL(tt) = 0
8.29/3.05	   POL(u) = 1
8.29/3.05	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.05	
8.29/3.05	   U31(tt, V) -> U32(isQid(V))
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(36)
8.29/3.05	Obligation:
8.29/3.05	Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U31: {1}
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(37) CSRRRRProof (EQUIVALENT)
8.29/3.05	The following CSR is given: Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U31: {1}
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	Used ordering:
8.29/3.05	Polynomial interpretation [POLO]:
8.29/3.05	
8.29/3.05	   POL(U11(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(U12(x_1)) = x_1
8.29/3.05	   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U22(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(U31(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
8.29/3.05	   POL(U42(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
8.29/3.05	   POL(a) = 1
8.29/3.05	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(e) = 1
8.29/3.05	   POL(i) = 1
8.29/3.05	   POL(isList(x_1)) = 1 + x_1
8.29/3.05	   POL(isNeList(x_1)) = 1 + x_1
8.29/3.05	   POL(isPalListKind(x_1)) = 0
8.29/3.05	   POL(nil) = 1
8.29/3.05	   POL(o) = 1
8.29/3.05	   POL(tt) = 0
8.29/3.05	   POL(u) = 1
8.29/3.05	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.05	
8.29/3.05	   isNeList(V) -> U31(isPalListKind(V), V)
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(38)
8.29/3.05	Obligation:
8.29/3.05	Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(39) CSRRRRProof (EQUIVALENT)
8.29/3.05	The following CSR is given: Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	__: {1, 2}
8.29/3.05	nil: empty set
8.29/3.05	U11: {1}
8.29/3.05	tt: empty set
8.29/3.05	U12: {1}
8.29/3.05	isNeList: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	U41: {1}
8.29/3.05	U42: {1}
8.29/3.05	and: {1}
8.29/3.05	isPalListKind: empty set
8.29/3.05	a: empty set
8.29/3.05	e: empty set
8.29/3.05	i: empty set
8.29/3.05	o: empty set
8.29/3.05	u: empty set
8.29/3.05	Used ordering:
8.29/3.05	Polynomial interpretation [POLO]:
8.29/3.05	
8.29/3.05	   POL(U11(x_1, x_2)) = x_1
8.29/3.05	   POL(U12(x_1)) = 1 + 2*x_1
8.29/3.05	   POL(U21(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + 2*x_3
8.29/3.05	   POL(U22(x_1, x_2)) = 2 + x_1 + 2*x_2
8.29/3.05	   POL(U41(x_1, x_2, x_3)) = 1 + 2*x_1 + 2*x_2 + 2*x_3
8.29/3.05	   POL(U42(x_1, x_2)) = x_1 + 2*x_2
8.29/3.05	   POL(__(x_1, x_2)) = 2 + 2*x_1 + 2*x_2
8.29/3.05	   POL(a) = 2
8.29/3.05	   POL(and(x_1, x_2)) = x_1 + x_2
8.29/3.05	   POL(e) = 2
8.29/3.05	   POL(i) = 2
8.29/3.05	   POL(isList(x_1)) = 2 + 2*x_1
8.29/3.05	   POL(isNeList(x_1)) = 0
8.29/3.05	   POL(isPalListKind(x_1)) = 1 + 2*x_1
8.29/3.05	   POL(nil) = 2
8.29/3.05	   POL(o) = 2
8.29/3.05	   POL(tt) = 2
8.29/3.05	   POL(u) = 2
8.29/3.05	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.05	
8.29/3.05	   U11(tt, V) -> U12(isNeList(V))
8.29/3.05	   U12(tt) -> tt
8.29/3.05	   U41(tt, V1, V2) -> U42(isList(V1), V2)
8.29/3.05	   and(tt, X) -> X
8.29/3.05	   isList(V) -> U11(isPalListKind(V), V)
8.29/3.05	   isPalListKind(a) -> tt
8.29/3.05	   isPalListKind(e) -> tt
8.29/3.05	   isPalListKind(i) -> tt
8.29/3.05	   isPalListKind(nil) -> tt
8.29/3.05	   isPalListKind(o) -> tt
8.29/3.05	   isPalListKind(u) -> tt
8.29/3.05	   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(40)
8.29/3.05	Obligation:
8.29/3.05	Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	tt: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(41) CSRRRRProof (EQUIVALENT)
8.29/3.05	The following CSR is given: Context-sensitive rewrite system:
8.29/3.05	The TRS R consists of the following rules:
8.29/3.05	
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	
8.29/3.05	The replacement map contains the following entries:
8.29/3.05	
8.29/3.05	tt: empty set
8.29/3.05	U21: {1}
8.29/3.05	U22: {1}
8.29/3.05	isList: empty set
8.29/3.05	Used ordering:
8.29/3.05	Matrix interpretation [MATRO] to (N^2, +, *, >=, >) :
8.29/3.05	
8.29/3.05	   <<<
8.29/3.05	 POL(U21(x_1, x_2, x_3)) =  	[[1]] 	 +  	[[1, 1]] 	* 	x_1 	 +  	[[1, 1]] 	* 	x_2 	 +  	[[1, 1]] 	* 	x_3
8.29/3.05	>>>
8.29/3.05	
8.29/3.05	   <<<
8.29/3.05	 POL(tt) =  	[[1], [1]]
8.29/3.05	>>>
8.29/3.05	
8.29/3.05	   <<<
8.29/3.05	 POL(U22(x_1, x_2)) =  	[[1]] 	 +  	[[1, 1]] 	* 	x_1 	 +  	[[1, 1]] 	* 	x_2
8.29/3.05	>>>
8.29/3.05	
8.29/3.05	   <<<
8.29/3.05	 POL(isList(x_1)) =  	[[1], [0]] 	 +  	[[1, 0], [0, 1]] 	* 	x_1
8.29/3.05	>>>
8.29/3.05	
8.29/3.05	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
8.29/3.05	
8.29/3.05	   U21(tt, V1, V2) -> U22(isList(V1), V2)
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(42)
8.29/3.05	Obligation:
8.29/3.05	Context-sensitive rewrite system:
8.29/3.05	R is empty.
8.29/3.05	
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(43) RisEmptyProof (EQUIVALENT)
8.29/3.05	The CSR R is empty. Hence, termination is trivially proven.
8.29/3.05	----------------------------------------
8.29/3.05	
8.29/3.05	(44)
8.29/3.05	YES
8.29/3.08	EOF